How can I remove these "steps" between faces from the mesh?
Go into edit mode. Hold your cursor over one of the long edges and hit 'Ctrl-R' to add an edge loop.  See where that loop is added. If it stops at the edge of the triangle, that is OK.  Keep adding edge loops between the top and bottom 'curves.' If the edge loops stopped at the triangles, do the same to the right and left 'legs,' with the same number of edge loops added.  Go into 'point/vertex' mode, select two points to bridge, and press 'F' to bridge them with an edge. You will have to subdivide edges in the middle of the triangles in order to get movable geometry in those areas. Continue doing this for a while and massaging the position of those points in XYZ space until you are happy with the surface flow.  That massaging can be done in edit mode, or you can jump over to sculpt mode.